The Standard Normal Distribution is a continuous distribution where the following exact ''areas'' are bound between the Standard Normal Density Function and the x-axis on the symmetric intervals around the origin:

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The Standard Normal Distribution is a continuous distribution with the following density:

* The Standard Normal distribution is also a special case of the [[AP_Statistics_Curriculum_2007_Normal_Prob | more general normal distribution]] where the mean is set to zero and a variance to one. The Standard Normal distribution is often called the ''bell curve'' because the graph of its probability density resembles a bell.

* The Standard Normal distribution is also a special case of the [[AP_Statistics_Curriculum_2007_Normal_Prob | more general normal distribution]] where the mean is set to zero and a variance to one. The Standard Normal distribution is often called the ''bell curve'' because the graph of its probability density resembles a bell.

Standard Normal Distribution

The Standard Normal Distribution is a continuous distribution with the following density:

Standard Normal density function

Note that the following exact areas are bound between the Standard Normal Density Function and the x-axis on these symmetric intervals around the origin:

The area: -1 < x < 1 = 0.8413 - 0.1587 = 0.6826

The area: -2.0 < x < 2.0 = 0.9772 - 0.0228 = 0.9544

The area: -3.0 < x < 3.0 = 0.9987 - 0.0013 = 0.9974

The Standard Normal distribution is also a special case of the more general normal distribution where the mean is set to zero and a variance to one. The Standard Normal distribution is often called the bell curve because the graph of its probability density resembles a bell.

Experiments

Suppose we decide to test the state of 100 used batteries. To do that, we connect each battery to a volt-meter by randomly attaching the positive (+) and negative (-) battery terminals to the corresponding volt-meter's connections. Electrical current always flows from + to -, i.e., the current goes in the direction of the voltage drop. Depending upon which way the battery is connected to the volt-meter we can observe positive or negative voltage recordings (voltage is just a difference, which forces current to flow from higher to the lower voltage.) Denote Xi={measured voltage for battery i} - this is random variable with mean of 0 and unitary variance. Assume the distribution of all Xi is Standard Normal, . Use the Normal Distribution (with mean=0 and variance=1) in the SOCR Distribution applet to address the following questions. This Distributions help-page may be useful in understanding SOCR Distribution Applet. How many batteries, from the sample of 100, can we expect to have?